All Questions
Tagged with pde computational-physics
23
questions
2
votes
1
answer
278
views
Asking advice for implementation of Conservative Finite Difference Scheme for numerically solving Gross-Pitaevskii equation
I am trying to numerically solve the Gross-Pitaevskii equation for an impurity coupled with a one-dimensional weakly-interacting bosonic bath, given by (in dimensionless units):
\begin{align}
i \frac{\...
- 21
2
votes
0
answers
108
views
How can we symbolically working out $\phi^4$ theory green's function/propagator and consequences in python?
I am having some difficulty calculating Green's function symbolically in Python for $\phi^4$ theory.
The specific rendition of the $\phi^4$ theory I have in mind can be written as follows.
$\mathcal{L}...
- 121
2
votes
2
answers
1k
views
Problems solving 2D heat equation using physics-informed neural networks
I am trying to solve 2D heat equation using the physics-informed neural networks approach. The training loss is decreasing, but my final network outputs make no sense. I am using Python/Pytorch.
2D ...
1
vote
0
answers
207
views
Solving PDE on a non-uniform grid with Crank-Nicolson scheme
I am solving a 1D diffusion-type equation with the finite-difference Crank-Nicolson (CN) scheme, and I need to densify the spatial grid around the central point. One could change the spatial variable ...
- 21
1
vote
1
answer
124
views
What FEM solver should be used for matrix-valued FE spaces?
I am pretty new to using FE solvers. I am trying to solve a system of (up to) 9 complex equations. We write these as a matrix equation (here), (with the implied sum over $j$, for each component ...
- 21
1
vote
0
answers
82
views
Finding the weak form of a PDE with a tensor argument
I am trying to solve for the order parameter ($A$) in the Ginzburg Landau equations. I had asked on the math SE site but was recommended to ask here.
We are trying to solve the following equation, (...
- 21
3
votes
1
answer
329
views
Finite element method for high-frequency electromagnetics
I am writing a project about the Finite element method for use in high-frequency solutions of Maxwell's equations. This could be for use in antenna design and similar.
I have some trouble ...
- 33
1
vote
0
answers
177
views
Integrating a wavelike equation with absorbing boundary conditions
I am trying to numerically solve the following equation:
$\frac{\partial^{2} \phi}{\partial t^{2}}-\frac{\partial^{2} \phi}{\partial x^{2}}+V(x) \phi(x, t)=0$ On some domain, with:
$\phi(x, 0) = I(x)$
...
- 111
0
votes
1
answer
99
views
Acoustic Simulation, how are boundaries handled?
I don't have a background in numerical modeling so this question is rather broad.
What I am interested in is modeling the propagation of an ultrasonic acoustic wave in 3d space. The basic 3d wave ...
- 133
2
votes
1
answer
132
views
Effect on methods like Crank-Nicolson of adding a potential term, changing heat equation to Schrodinger equation
I'm studying up on methods for numerically solving the Schrodinger equation. The Schrodinger equation with a zero potential is formally identical to the heat equation in the sense that we just make ...
user28109
1
vote
1
answer
75
views
How long should the hyperelastic equations be solved before updating the mesh?
How long should the hyperelastic equations be solved before updating the mesh? To be specific, I'm interested in the hyperelastic model with a neo-Hookean solid:
$$
\nabla\cdot\sigma + f = \rho\ddot{...
- 767
3
votes
3
answers
405
views
What numerical methods are used to model deformations in elastic physics?
What numerical methods are used to model deformations in elastic physics? For example, here's an example of a hyperelastic deformation in Ansys:
Perhaps more simply than hyperelasticity, for linear ...
- 767
4
votes
2
answers
2k
views
How to simulate basic semiconductor models using the Drift-diffusion model on Python?
I'm trying to simulate basic semiconductor models for pedagogical purposes--starting from the Drift-diffusion model. Although I don't want to use an off-the-shelf semiconductor simulator--I'll be ...
- 41
1
vote
0
answers
141
views
Finite difference methods for coupled 2nd order nonlinear pdes
I have a system of coupled nonlinear PDEs that I cannot figure out how to solve in a smart way using FDM, so I was hoping someone here might have a clue.
The equations go as:
\begin{align*}
\frac{1}{...
- 95
1
vote
0
answers
68
views
Jacobian Elements for Coupled Drift-Diffusion System using Vertex-Centered Finite Volume
I'm trying to solve the fully coupled drift-diffusion system using Newton's Method. Although I eventually plan to potentially use a Jacobian-Free Newton-Krylov approach, this is still something that I ...
- 321